Grade 8 - Mathematics5.1 Theorem - I

Theorem:
The sum or difference of any two even numbers is an even number.

Proof:
An even number is a number which leaves remainder '0' when divided by 2.
The general form of an even number is 2n, where n is an integer.
Let 2m and 2n are any two numbers, m and n are integers.
Their sum = 2m+2n
= 2(m+n)
= 2 * an integer [ Since, m+n = an integer ]
= 2 * l
If 'l' is odd or even but 2l is always even.
Difference of two even numbers.
2m-2n = 2(m-n)
= 2 * an integer.
= 2 * p
If 'p' is odd or even but 2p is always even.